Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 6x - 1$ and $ KL = 2x + 31$ Find $JL$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {6x - 1} = {2x + 31}$ Solve for $x$ $ 4x = 32$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 6({8}) - 1$ $ KL = 2({8}) + 31$ $ JK = 48 - 1$ $ KL = 16 + 31$ $ JK = 47$ $ KL = 47$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {47} + {47}$ $ JL = 94$